Inertial forward-backward splitting method in Banach spaces with application to compressed sensing

By Prasit Cholamjiak, Yekini Shehu. Applied Mathematics, 2019

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We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the lew available inertial-type methods for zeros of the sum of accretive operators in Banach spaces.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/53406811bd74f7f262f97a0bade1417b2c7a5bbd